DOCSLIB.ORG

Kondo Destruction and Quantum Criticality in Kondo Lattice Systems

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Kondo Destruction and Quantum Criticality in Kondo Lattice Systems J. Phys. Soc. Jpn. Downloaded from journals.jps.jp by Rice University on 06/01/17 Journal of the Physical Society of Japan 83, 061005 (2014) Special Topics http://dx.doi.org/10.7566/JPSJ.83.061005 Advances in Physics of Strongly Correlated Electron Systems Kondo Destruction and Quantum Criticality in Kondo Lattice Systems Qimiao Si1+, Jedediah H. Pixley1, Emilian Nica1, Seiji J. Yamamoto1, Pallab Goswami2, Rong Yu3, and Stefan Kirchner4,5 1Department of Physics and Astronomy, Rice University, Houston, TX 77005, U.S.A. 2National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32310, U.S.A. 3Department of Physics, Renmin University of China, Beijing 100872, China 4Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany 5Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany (Received December 3, 2013; accepted December 26, 2013; published online May 9, 2014) Considerable efforts have been made in recent years to theoretically understand quantum phase transitions in Kondo lattice systems. A particular focus is on Kondo destruction, which leads to quantum criticality that goes beyond the Landau framework of order-parameter fluctuations. This unconventional quantum criticality has provided an understanding of the unusual dynamical scaling observed experimentally. It also predicted a sudden jump of the Fermi surface and an extra (Kondo destruction) energy scale, both of which have been verified by systematic experiments. Considerations of Kondo destruction have in addition yielded a global phase diagram, which has motivated the current interest in heavy fermion materials with variable dimensionality or geometrical frustration. Here we summarize these developments, and discuss some of the ongoing work and open issues. We also consider the implications of these results for superconductivity. Finally, we address the effect of spin–orbit coupling on the global phase diagram, suggest that SmB6 under pressure may display unconventional superconductivity in the transition regime between a Kondo insulator phase and an antiferroamgnetic metal phase, and argue that the interfaces of heavy-fermion heterostructures will provide a fertile setting to explore topological properties of both Kondo insulators and heavy- fermion superconductors. 1. Introduction Quantum criticality is currently being studied in a wide variety of strongly correlated electron systems. It provides a mechanism for both non-Fermi liquid excitations and unconventional superconductivity. Heavy fermion metals represent a prototype system to study the nature of quantum criticality, as well as the novel phases that emerge in the vicinity of a quantum critical point (QCP).1,2) Over the past decade, Kondo lattice systems have provided a setting for extensive theoretical analysis of quantum phase transitions between ordered antiferromagnetic (AF) and paramagnetic ground states. Various studies have revealed a class of unconventional QCPs that goes beyond the Landau framework of order-parameter fluctuations. This local Fig. 1. (Color online) Quantum critical behavior in the generic phase diagram of temperature and a non-thermal control parameter. quantum criticality incorporates the physics of Kondo destruction. Considerations of unconventional quantum criticality have naturally led to the question of the role of symmetry of the Hamiltonian, and is therefore a magneti- Kondo destruction in the emergent phases. Consequently, a cally-disordered state. global phase diagram has recently been proposed. In general, the ratio of such competing interactions In this article, we give a perspective on this subject and specifies a control parameter, which tunes the system from discuss the recent developments. We also point out several one ground state to another through a quantum phase outstanding issues and some new avenues for future studies. transition. A typical case is illustrated in Fig. 1, where the quantum phase transition goes from an ordered state to a 2. Quantum Criticality disordered one. When it is continuous, the transition occurs at A quantum many-body Hamiltonian may contain terms a QCP. that lead to competing ground states. A textbook example3,4) In the Landau framework, the phases are distinguished is the problem of a chain of Ising spins, containing both a by an order parameter, which characterizes the spontaneous nearest-neighbor ferromagnetic exchange interaction between symmetry breaking. The quantum criticality is then described the spins and a magnetic field applied along a transverse in terms of d þ z-dimensional fluctuations of the order direction. The exchange interaction favors a ground state in parameter in space and time. Here, d is the spatial dimension which all the spins are aligned, which spontaneously breaks a and z is the dynamic exponent. global Z2 symmetry and yields the familiar ferromagnetic For weak metallic antiferromagnets, the magnetization order. The transverse field, on the other hand, prefers a associated with the ordering wavevector characterizes a spin- ground state in which all the spins point along the transverse density-wave (SDW) order. The QCP separates the SDW direction; this state does not spontaneously break any phase from a paramagnetic Fermi liquid state. The collective 061005-1 ©2014 The Physical Society of Japan J. Phys. Soc. Jpn. Downloaded from journals.jps.jp by Rice University on 06/01/17 J. Phys. Soc. Jpn. 83, 061005 (2014) Special Topics Q. Si et al. is lowered. The RG flow is towards a strong-coupling fixed point, which controls the physics below a bare Kondo energy 0 À1 expð1 Þ scale: TK 0 =0JK , where 0 is the density of states of the conduction electrons at the Fermi energy. At the fixed point, the local moment and the spins of the conduction electrons are locked into an entangled singlet state: 1 j i¼ ðj"i j#i À j#i j"i Þ ð3Þ Kondo singlet 2 f c,FS f c,FS ; δ j i where c,FS represents a linear combination of the conduction-electron states close to the Fermi energy. This singlet ground state supports a resonance in the low- energy electronic excitation spectrum. The Kondo resonance can clearly be seen in an analysis of the strong-coupling limit, when JK is taken to be larger than the bandwidth of the conduction electrons and, for the physical case of small JK, has been readily described in terms of a slave boson method.14) The Kondo coupling is converted into an effective δ à hybridization, b , between an emergent fermion f and the conduction electrons. Fig. 2. (Color online) Local quantum criticality (top panel) and the ¤ corresponding -dependence of the quasiparticle spectral weights zS and 3.2 Kondo lattice and heavy Fermi liquid zL, respectively for small and large Fermi surfaces (bottom panel). Here, 0 T =I is the control parameter, and T0 marks the initial onset of the In stoichiometric heavy fermion compounds containing, K fi 4 Kondo screening process; TN and TFL are respectively the Néel and Fermi- e.g., Ce or Yb elements, the partially- lled f electrons are à liquid temperatures. Eloc characterizes the Kondo destruction, separating the strongly correlated. They behave as a lattice of effective spin- part of the phase diagram where the system flows towards a Kondo-singlet 1/2 local moments, which describe the magnetic degrees of fl ground state from that where the ow is towards a Kondo-destroyed ground freedom of the lowest Kramers-doublet atomic levels. This state. The bottom panel also illustrates the small (left) and large (right) Fermi surfaces, and the fluctuating Fermi surfaces (middle) associated with the yields a Kondo lattice Hamiltonian: X X QCP. ¼ þ S Á S þ S Á sc ð4Þ HKL H0 Iij i j JK i i : ij i 4 fluctuations are described in terms of a theory of order- The Kondo coupling JK is antiferromagnetic and we will 5) parameter fluctuations. focus on an antiferromagnetic RKKY interaction, Iij > 0. In heavy fermion metals, QCPs between an AF phase and At high energies, the local moments are essentially a paramagnetic heavy-fermion state have been observed in decoupled, and Eq. (2) would continue to apply, signifying a number of compounds.1,2) The local quantum criticality the initial development of Kondo screening process. What (Fig. 2) has new critical modes associated with the happens in the ground state, however, will depend on the destruction of the Kondo effect, in addition to the fluctuations competition between the Kondo and RKKY interactions. of the AF order parameter.6,7) It has provided an under- Consider first the regime where the Kondo effect 0 standing of unusual dynamical scaling properties observed dominates, with TK being much larger than the RKKY in quantum critical heavy fermion metals,8,9) and made interaction. The physics of this regime can be inferred by predictions regarding the evolution of Fermi surfaces and taking the bare Kondo coupling JK to be greater than the emergence of new energy scales that have been verified by bandwidth W of the conduction electrons.15–17) The Fermi 10–13) subsequent experiments in YbRh2Si2 and CeRhIn5. surface will be large, enclosing 1 þ x electrons per unit cell. When JK=W is reduced to being considerably smaller than 1, 3. From the Kondo Effect to its Destruction 0 while keeping I=TK small, continuity dictates that the 3.1 Kondo effect entangled Kondo singlet state still characterize the ground The Kondo effect was originally studied in the context of a state, and the Fermi surface will remain large. This can be single-impurity Kondo model: seen, microscopically, through the slave-boson ap- 18–20) c proach. The Kondo resonance in the excitation spectrum HKondo ¼ H0 þ JKS Á s0: ð1Þ P appears as a pole in the conduction-electron self-energy: y c y Here, H0 ¼ k "kck ck, s0 ¼ c0 ð0 =2Þc00 , with à 2 ; y ðb Þ denoting a vector of Pauli matrices, and c creates an Æðk Þ¼ ð5Þ 0 ;! À à ; electron of spin · at the impurity site 0; the Kondo coupling ! "f JK is antiferromagnetic (JK > 0).
Load more

Recommended publications
  • Many-Body Effects in Optical Excitations of Transition Metal Dichalcogenides
    Research Collection Doctoral Thesis Many-Body Effects in Optical Excitations of Transition Metal Dichalcogenides Author(s): Sidler, Meinrad Publication Date: 2018-02 Permanent Link: https://doi.org/10.3929/ethz-b-000290909 Rights / License: In Copyright - Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use. ETH Library DISS. ETH NO. 24988 Many-Body Effects in Optical Excitations of Transition Metal Dichalcogenides A thesis submitted to attain the degree of DOCTOR OF SCIENCES of ETH ZURICH (Dr. sc. ETH Zurich) presented by MEINRAD SIDLER MSc ETH Physics, ETH Zurich born on 21.06.1989 citizen of Grosswangen LU accepted on the recommendation of: Prof. Ata¸cImamo˘glu,examiner Prof. Bernhard Urbaszek, co-examiner 2018 c Summary This dissertation treats a quantum impurity problem in a semiconductor system. Quantum impurity problems describe the interaction between a single quantum object and a complex environment. They are ubiquitous in physical systems and represent a fundamental field of research in many-body physics. Prominent examples are the Anderson orthogonality catastrophe and the Kondo effect. In both cases, the impurity is much heavier than the constituents of the interacting environment. If the mass of the impurity is comparable to the surrounding particles, we have a mobile impurity. These systems are usually harder to solve, as evident in the case of lattice polarons, which were first proposed in 1933 by Lev Landau. A complex but accurate description was found years later in 1955 by Richard Feynman. In recent years, strong coupling between single, mobile quantum impurities and a fermionic bath was realized in cold atoms.
    [Show full text]
  • A New View on the Origin of Zero-Bias Anomalies of Co Atoms Atop Noble Metal Surfaces ✉ ✉ Juba Bouaziz 1 , Filipe Souza Mendes Guimarães 1 & Samir Lounis 1
    ARTICLE https://doi.org/10.1038/s41467-020-19746-1 OPEN A new view on the origin of zero-bias anomalies of Co atoms atop noble metal surfaces ✉ ✉ Juba Bouaziz 1 , Filipe Souza Mendes Guimarães 1 & Samir Lounis 1 Many-body phenomena are paramount in physics. In condensed matter, their hallmark is considerable on a wide range of material characteristics spanning electronic, magnetic, thermodynamic and transport properties. They potentially imprint non-trivial signatures in 1234567890():,; spectroscopic measurements, such as those assigned to Kondo, excitonic and polaronic features, whose emergence depends on the involved degrees of freedom. Here, we address systematically zero-bias anomalies detected by scanning tunneling spectroscopy on Co atoms deposited on Cu, Ag and Au(111) substrates, which remarkably are almost identical to those obtained from first-principles. These features originate from gaped spin-excitations induced by a finite magnetic anisotropy energy, in contrast to the usual widespread inter- pretation relating them to Kondo resonances. Resting on relativistic time-dependent density functional and many-body perturbation theories, we furthermore unveil a new many-body feature, the spinaron, resulting from the interaction of electrons and spin-excitations loca- lizing electronic states in a well defined energy. ✉ 1 Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, Jülich 52425, Germany. email: [email protected]; [email protected] NATURE COMMUNICATIONS | (2020) 11:6112 | https://doi.org/10.1038/s41467-020-19746-1 | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-19746-1 ignatures of many-body phenomena in solid state physics theoretical transport spectra are nearly identical to the experi- Sare diverse1–5.
    [Show full text]
  • Kondo Effect in Mesoscopic Quantum Dots
    1 Kondo Effect in Mesoscopic Quantum Dots M. Grobis,1 I. G. Rau,2 R. M. Potok,1,3 and D. Goldhaber-Gordon1 1 Department of Physics, Stanford University, Stanford, CA 94305 2 Department of Applied Physics, Stanford University, Stanford, CA 94305 3 Department of Physics, Harvard University, Cambridge, MA 02138 Abstract A dilute concentration of magnetic impurities can dramatically affect the transport properties of an otherwise pure metal. This phenomenon, known as the Kondo effect, originates from the interactions of individual magnetic impurities with the conduction electrons. Nearly a decade ago, the Kondo effect was observed in a new system, in which the magnetic moment stems from a single unpaired spin in a lithographically defined quantum dot, or artificial atom. The discovery of the Kondo effect in artificial atoms spurred a revival in the study of Kondo physics, due in part to the unprecedented control of relevant parameters in these systems. In this review we discuss the physics, origins, and phenomenology of the Kondo effect in the context of recent quantum dot experiments. After a brief historical introduction (Sec. 1), we first discuss the spin-½ Kondo effect (Sec. 2) and how it is modified by various parameters, external couplings, and non-ideal conduction reservoirs (Sec. 3). Next, we discuss measurements of more exotic Kondo systems (Sec. 4) and conclude with some possible future directions (Sec. 5). Keywords Kondo effect, quantum dot, single-electron transistor, mesoscopic physics, Anderson model, Coulomb blockade, tunneling transport, magnetism, experimental physics 2 1 Introduction At low temperatures, a small concentration of magnetic impurities — atoms or ions with a non-zero magnetic moment — can dramatically affect the behavior of conduction electrons in an otherwise pure metal.
    [Show full text]
  • Kondo Effect in Real Metals Ph
    Kondo effect in real metals Ph. Nozières, Annie Blandin To cite this version: Ph. Nozières, Annie Blandin. Kondo effect in real metals. Journal de Physique, 1980, 41 (3), pp.193- 211. 10.1051/jphys:01980004103019300. jpa-00209235 HAL Id: jpa-00209235 https://hal.archives-ouvertes.fr/jpa-00209235 Submitted on 1 Jan 1980 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. J. Physique 41 (1980) 193-2111 MARS 1980, 193 Classification Physics Abstracts 75.20H Kondo effect in real metals Ph. Nozières Institut Laue-Langevin, 156X, 38042 Grenoble Cedex, France and A. Blandin Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, France (Reçu le 21 septembre 1979, accepte le 30 octobre 1979) Résumé. 2014 Dans le cadre d’un hamiltonien d’Anderson généralisé, nous étudions le comportement d’une impureté magnétique dans un métal réel, compte tenu de la structure orbitale des électrons localisés sur l’impureté, du champ cristallin et du couplage spin-orbite. Nous nous limitons à un schéma atomique, dans lequel l’impureté a une valeur bien définie entière (une transformation de Schrieffer Wolff est alors possible). Les principales étapes d’une procédure de renormalisation sont décrites en détail.
    [Show full text]
  • Heavy Fermions: Electrons at the Edge of Magnetism
    Heavy Fermions: Electrons at the Edge of Magnetism Piers Coleman Rutgers University, Piscataway, NJ, USA Mathur et al., 1998). The ‘quantum critical point’ (QCP) that 1 Introduction: ‘Asymptotic Freedom’ in a Cryostat 95 separates the heavy-electron ground state from the AFM rep- 2 Local Moments and the Kondo Lattice 105 resents a kind of singularity in the material phase diagram 3 Kondo Insulators 123 that profoundly modifies the metallic properties, giving them a a predisposition toward superconductivity and other novel 4 Heavy-fermion Superconductivity 126 states of matter. 5 Quantum Criticality 135 One of the goals of modern condensed matter research 6 Conclusions and Open Questions 142 is to couple magnetic and electronic properties to develop Notes 142 new classes of material behavior, such as high-temperature Acknowledgments 142 superconductivity or colossal magnetoresistance materials, References 143 spintronics, and the newly discovered multiferroic materials. Further Reading 148 Heavy-electron materials lie at the very brink of magnetic instability, in a regime where quantum fluctuations of the magnetic and electronic degrees are strongly coupled. As such, they are an important test bed for the development of 1 INTRODUCTION: ‘ASYMPTOTIC our understanding about the interaction between magnetic FREEDOM’ IN A CRYOSTAT and electronic quantum fluctuations. Heavy-fermion materials contain rare-earth or actinide The term heavy fermion was coined by Steglich et al. (1976) ions, forming a matrix of localized magnetic moments. The in the late 1970s to describe the electronic excitations in active physics of these materials results from the immersion a new class of intermetallic compound with an electronic of these magnetic moments in a quantum sea of mobile con- density of states as much as 1000 times larger than copper.
    [Show full text]
  • Kondo Effect in Quantum Dots
    Kondo Effect in Quantum Dots Seminar: Nanoscopic Systems 29. 7. 2005 Gesa von Bornstaedt Gesa von Bornstaedt Kondo Effect in Quantum Dots Outline 1. What is the Kondo effect? 2. Calculation of the Kondo effect for a single magnetic impurity 3. ”Poor Man’s Scaling” - A renormalization group approach 4. Investigation of the Kondo effect in quantum dots 5. Conclusion Gesa von Bornstaedt Kondo Effect in Quantum Dots 1. What is the Kondo effect? • Resistivity is dominated by phonon scattering for T 0 • In most metals the resistivity decreases monotonically for T → 0 • But: resistance minimum in some metals for T → 0 • Kondo effect: Resonant spin flip scattering at local magnetic impurities • Influences transport properties Figure 1: Minimum in the resistivity of Au (de Haas, de Boer and van den Berg, 1934) Gesa von Bornstaedt Kondo Effect in Quantum Dots 2. Calculation for a single local magnetic impurity Hamiltonian Kondo’s assumption: a local magnetic moment associated with a spin S which is coupled via an exchange interaction with the conduction band electron. † 1 + − − + H = ∑kckσ ckσ + J(ω) S s + S s + Jz(ω)Szsz kσ 2 † 1 + † − † † † = ∑kckσ ckσ + ∑ J(ω) S ck↓ck0↑ + S ck↑ck0↓ + Jz(ω)Sz ck↑ck0↑ − ck↓ck0↓ kσ 2 k,k0 S = local impurity spin s = conduction electron spin Figure 2: Spin flip scattering of a localized impurity moment by a conduction electron Gesa von Bornstaedt Kondo Effect in Quantum Dots Perturbative approach • T > 0 =⇒ expectation values can’t be taken with respect to the ground state • Appropriate: Matsubara Method Starting
    [Show full text]
  • A High-Temperature Silicon Qubit and Its Quantum Interference Tunable
    Abstracts from Invited Speakers Keiji Ono (RIKEN) A High-temperature Silicon Qubit and its Quantum Interference Spin qubits are attractive building blocks for quantum computers. Si is a promising host material for spin qubits since it could enable long coherence, high-density integration, and high compatibility with classical computers. Spin qubits have been implemented in Si using gate-defined quantum dots or shallow impurities. However, these qubits must be operated at temperatures <0.1 K, limiting the expansion of qubit technology. We used deep impurities in Si to achieve room-temperature single- electron tunnelling and spin qubit operation at 5–10 K [1]. We employed tunnel field-effect transistors (TFETs) instead of conventional metal–oxide–semiconductor field-effect transistors and achieved strong confinement of the single quantum dots embraced in TFETs up to 0.3 eV. Furthermore, double- quantum-dot devices were operated as spin qubits, and read-out was realized using a spin blockade. These results will enable broadening of the range of spin qubit applications such as sensing, security, and quantum computing. We also study quantum interference effects of a qubit whose energy levels are continuously modulated [2]. The qubit energy levels are modulated via its gate-voltage-dependent g-factors, with either rectangular, sinusoidal, or ramp radio-frequency waves. The energy-modulated qubit is probed by the electron spin resonance. Our results demonstrate the potential of spin qubit interferometry that is implemented in a Si device and is operated at a relatively high temperature. [1] K. Ono, T. Mori, S. Moriyama, High-Temperature Operation of Spin Qubits based on Silicon Tunnel Field-Effect Transistors, arXiv:1804.03364, Scientific reports, in print.
    [Show full text]
  • Arxiv:1102.2798V1 [Cond-Mat.Mes-Hall] 14 Feb 2011 Ipysprse Yculn Ftesi Omolecu- to Spin the of One Be Coupling to by [8]
    Interaction of spin and vibrations in transport through single-molecule magnets F. May(1,2), M. R. Wegewijs(3,4), and W. Hofstetter(1) (1) Institut f¨ur Theoretische Physik, Johann Wolfgang Goethe-Universit¨at, 60438 Frankfurt/Main, Germany (2) Max Planck Institute for Polymer Research, 55128 Mainz, Germany (3) Institut f¨ur Theorie der Statistischen Physik, RWTH Aachen, 52056 Aachen, Germany and (4) Peter Gr¨unberg Institut and JARA - Fundamentals of Information Technology, Forschungszentrum J¨ulich, 52425 J¨ulich, Germany We study linear electron transport through a single-molecule magnet (SMM) and the interplay of its anisotropic spin with quantized vibrational distortions of the molecule. We show that, despite the longitudinal anisotropy barrier and small transverse anisotropy, vibrational fluctuations can induce quantum spin-tunneling (QST) and a QST-Kondo effect. The interplay of spin scattering, QST and molecular vibrations can strongly enhance the Kondo effect and induce an anomalous magnetic field dependence of vibrational Kondo side-bands. PACS numbers: 85.65.+h, 73.63.Kv, 85.35.-p Transport measurements on nanometer-sized magnetic lar vibrations as this tends to increase the anisotropy systems address the fundamental problem of how a few barrier [7]. However, the dynamical effect of vibrational magnetic atoms in an anisotropic environment respond to fluctuations and the possible competition between longi- an electron current [1]. Such an environment is provided, tudinal and transverse spin-vibration coupling have not for instance, by ligand groups holding such atoms to- been studied so far, even though coupling to vibrations in gether in a single magnetic molecule contacted in a break the Kondo regime has been considered for spin-isotropic junction [2, 3].
    [Show full text]
  • Interplay Between Charge, Magnetic and Superconducting Order in a Kondo Lattice with an Attractive Hubbard Interaction
    Interplay between charge, magnetic and superconducting order in a Kondo lattice with an attractive Hubbard interaction Benedikt Lechtenberg,1 Robert Peters,1 and Norio Kawakami1 1Department of Physics, Kyoto University, Kyoto 606-8502, Japan (Dated: May 8, 2019) We investigate the competition between superconductivity, charge-ordering, magnetic-ordering, and the Kondo effect in a heavy fermion s-wave superconductor described by a Kondo lattice model with an attractive on-site Hubbard interaction. The model is solved using the real-space dynamical mean field theory. For this purpose, we develop a numerical renormalization group (NRG) framework in Nambu space, which is used to solve the superconducting impurity problem. This extended NRG scheme also allows for SU(2) spin symmetry broken solutions, enabling us to examine the competition or cooperation between s-wave superconductivity and incommensurate spin-density waves (SDWs). At half filling, we find an intriguing phase where the magnetic ordering of the f-electrons lifts the degeneracy between the charge density wave (CDW) state and the superconducting state, leading to a strong suppression of superconductivity. In addition, the system may also become a half metal in this parameter regime. Away from half filling, the CDWs vanish and are replaced by superconductivity combined with incommensurate SDWs up to moderate Kondo couplings to the f-electrons. We find that both CDWs as well as superconductivity enhance magnetic ordering due to the suppression of Kondo screening. I. INTRODUCTION the interplay between superconductivity, magnetic order- ing, charge ordering, and the Kondo effect. One of the simplest models comprising all these effects Strongly correlated electron systems attract enormous is a Kondo lattice [37{41] with an additional attractive attention because of the multitude of remarkable phe- Hubbard interaction U < 0 [42]: nomena they exhibit, such as the Kondo effect, mag- netic or charge ordering, and unconventional supercon- X y X H =t c c + H:c: µ ni,σ ductivity.
    [Show full text]
  • Tuning the Kondo Effect in Yb (Fe1−X Cox)2 Zn20
    Physics and Astronomy Publications Physics and Astronomy 4-15-2017 Tuning the Kondo effect in Yb (Fe1−x Cox)2 Zn20 Tai Kong Iowa State University and Ames Laboratory Valentin Taufour Iowa State University and Ames Laboratory Sergey L. Bud’ko Iowa State University and Ames Laboratory, [email protected] Paul C. Canfield Iowa State University and Ames Laboratory, [email protected] Follow this and additional works at: https://lib.dr.iastate.edu/physastro_pubs Part of the Condensed Matter Physics Commons The complete bibliographic information for this item can be found at https://lib.dr.iastate.edu/physastro_pubs/523. For information on how to cite this item, please visit http://lib.dr.iastate.edu/howtocite.html. This Article is brought to you for free and open access by the Physics and Astronomy at Iowa State University Digital Repository. It has been accepted for inclusion in Physics and Astronomy Publications by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Tuning the Kondo effect in Yb (Fe1−x Cox)2 Zn20 Abstract We study the evolution of the Kondo effect in heavy fermion compounds, Yb(Fe1−xCox)2Zn20 (0≤x≤1), by means of temperature-dependent electric resistivity and specific heat. The ground state of YbFe2Zn20 can be well described by a Kondo model with degeneracy N = 8 and a TK∼30 K. The ground state of YbCo2Zn20 is close to a Kondo state with degeneracy N = 2 and a much lower TK∼ 2 K, even though the total crystalline electric field (CEF) splittings are similar for YbFe2Zn20 and YbCo2Zn20.
    [Show full text]
  • A Holographic Model of the Kondo Effect
    A holographic model of the Kondo effect Johanna Erdmenger Max-Planck-Institut für Physik, München Based on joint work with C. Hoyos (Tel Aviv Univ.), A. O’Bannon (DAMTP Cambridge), J. Wu (NCTS Taiwan) 1309.xxxx, to appear Outline • 1. Kondo effect: Physics, CFT approach, large N • 2. Holographic model: Similarities and differences Kondo effect Screening of a magnetic impurity by conduction electrons at low temperatures Metals: Fermi liquid + impurities: In the presence of magnetic impurities: UV Free electrons + impurity spin IR Impurity screened Kondo model Kondo ’64, Affleck+Ludwig ‘90s Free electrons Local interaction with magnetic impurity Logarithmic behaviour at low temperatures Jun Kondo: • Progress of Theoretical Physics • Volume 32, Issue 1 • Pp. 37-49 TK : Kondo temperature IR theory is strongly coupled! TK ~ ΛQCD RG flow The Kondo model was decisive in the development of the RG formalism. (Wilson) Negative beta function: β λ2 + (λ3) λ ∝− O UV fixed point: Free theory Asymptotic freedom In some cases, the model flows to a strongly coupled IR fixed point. UV IR CFT approach Affleck+Ludwig, 90’s • One-impurity problem: Spherical symmetry • Reduces to 1+1-dimensional system with boundary • Consider only left-movers ψL ψL ψL ψR CFT approach Compare CFT’s at UV and IR fixed points UV: Free fermions, boundary condition ψ = ψ+ − IR: Free fermions, boundary condition ψ = ψ+ − − Change in boundary condition induces change in spectrum Generalizations Sugawara construction: Separation of spin, channel and charge currents IR CFT Critical, under- and overscreening Example of SU(2) k : Large N: Slave fermions χ†χ = q, Q = q/N Large N: Slave fermions Sachdev, Senthil, Voijta cond-mat/0209144 Kondo effect corresponds to condensation of = ψ† χ O L 2.
    [Show full text]
  • Topics in Kondo Insulators
    TOPICS IN KONDO INSULATORS By ARI WUGALTER A dissertation submitted to the School of Graduate Studies Rutgers, The State University of New Jersey In partial fulfillment of the requirements For the degree of Doctor of Philosophy Graduate Program in Physics and Astronomy Written under the direction of Piers Coleman And approved by New Brunswick, New Jersey October, 2020 ABSTRACT OF THE DISSERTATION Topics in Kondo Insulators By ARI WUGALTER Dissertation Director: Piers Coleman We have studied Kondo insulator states in the single and two-channel Kondo models. The Kondo insulator state shows remarkable optical properties. Specifically, a dielec- tric constant which is 100 times higher than for a regular insulator. Moreover, the ≈ diamagnetic permeability does not seem to be affected by the onset of the Kondo effect. This suggest that while the Kondo effect is very effective in suppressing the longitudinal current fluctuations, it is largely ineffective in its influence on diamag- netic currents. In the two channel Kondo model, we observe the formation of a half-Kondo insula- tor, where the spontaneous breaking of channel symmetry leads to the formation of a Kondo insulator in one channel, while the other channel remains metallic. We discuss, how this phenomenon can be understood using the concept of order fractionalization, in which the channel magnetization breaks up into an emergent spinor order para- meter. By integrating out the fermions we derive an effective action that describes this symmetry breaking and its emergent collective modes. A remarkable observation ii is that topological defects in the order parameter carry a U(1) flux, manifested in the Aharonov-Bohm phase picked by electrons that orbit the defect.
    [Show full text]